If you do have access to the private key of the address you have sent your funds to, you should be able to recover your funds buy exporting the private key out of your current wallet + importing it into a LTC wallet.

If you, on the other hand, do NOT have access to the private key, you will need to contact the person who is in control of 'your' address. They are able to recover the funds. But depending on which kind of exchange / web wallet it is, this is rather unlikely.